Data analysis of low SNR signals in fast high‚ÄövÑv™noise acquisition systems and validation with miniaturised electrophoresis

This thesis describes three areas of work and study; the first being experimental and instrumental, and the second two being the deriving of mathematical and numerical processes. All three areas deal with the vexed question of low concentration analyte signals within high noise backgrounds. The first area of work deals with the design and construction of a small-scale compact sequential injection ‚Äö- capillary electrophoresis (SI-CE) apparatus to detect low concentrations (<100 ppb) of heavy metals. Various configurations of inexpensive components included small-scale pumps, valves, switches, miniaturised 3 kV HV units, monochromatic LEDs, and a 10-bit Arduino UNO\\(^{TM}\\) control system were tested. In its final configuration, the instrument occupied a volume of 20x13x10 cm\\(^3\\), with mass approximately 900 g. This instrument cost less than $AU1000, and was able to operate independently on a drill battery for three days. The battery-powered operation (n=1163 runs) showed consistent migration times and areas with RSDs < 2.0% and 9.0%, respectively. It was then shown to be able to detect lead levels in the low (<10 ppb) range, by pre-capillary complexation with PAR. The instrument was then calibrated against commercial (Agilent) instrumentation by separation of selected fluorophores. During the construction and trial of this instrument, it became clear that a 10 bit ADC gave a very noisy and rough signal particularly at low concentration, and in order to reduce noise it was necessary to introduce smoothing software into the real-time data processing of the ADC. This problem lead to noise reduction by means of oversampling, using a novel application of the Nyquist Theorem and using a snapshot approach to smoothing. Without this Nyquist smoothing approach, the instrument would not have been of much use without using higher-end components, leading to considerable increase in cost, size and complexity. The second body of work originated from ideas which come from smoothing of signals in the small-scale instrument. It is a comparative study of six different smoothing algorithms applied post-facto to unsmoothed datasets obtained from the previously developed instrument, and this resulted in a rank ordering of the algorithms according to performance on SNR, peak width and resolution over a range of smoothing window sizes. It was decided to use the three best performing algorithms out of the set of six for further study. The third body of work is an extension of the second and it involves deriving a novel method for using 2 algorithms of different mathematical structure and different optimal smoothing window sizes to smooth datasets with very high noise, very low SNR and very fast DAQs of the order 3 kHz and above. These latter datasets used for testing the methods were obtained from independent sources and contained completely hidden and unknown signals. The method uses these pairs of algorithms simultaneously and not successively, and significant improvements in performance on SNR, peak width and resolution when compared to the best-performing algorithm in each pair were obtained. The simultaneous-algorithm smoothing method has shown some demonstrable advantages in its ability to extract greater signal information from high-density, low SNR fast DAQ datasets by post-facto data processing using open source software. Finally, the potential application of such programmable mathematical techniques to the further development of more efficient small-scale inexpensive instrumentation is discussed.